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Proof step 4 from proof sis-neg-lower (previous step)

¬(i < 0 ∧ i % 65536 < ~32768), i < ~32768, ~65536 < i, i < 0 ⊦ s2i(i2s(i)) = i + 65536

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i < ~32768, ~65536 < i, i < 0, ~32768 ≤ i % 65536, i < i % 65536 ⊦ i % 65536 = i + 65536

Rule argument

Additional information

Used simplifier rules: sis-neg-high: ⊦ i < 0 ∧ ~32768 ≤ i % 65536 → s2i(i2s(i)) = i % 65536;% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ ¬ i < j ↔ j ≤ i;